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We consider a parabolic equation which describes the gravitational interaction of particles. Existence of solutions and their convergence to stationary states are studied.

A multiplicity result for the Schrodinger-Maxwell equations with negative potential

Giuseppe Maria Coclite (2002)

Annales Polonici Mathematici

We prove the existence of a sequence of radial solutions with negative energy of the Schrödinger-Maxwell equations under the action of a negative potential.

A note on a 3-dimensional stationary Schrödinger-Poisson system.

Benmlih, Khalid (2004)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A note on weighted estimates for the Schrödinger operator.

Juan A. Barceló, Jonathan M. Bennett, Anthony Carbery, Alberto Ruiz, M. Cruz Vilela (2008)

Revista Matemática Complutense

A numerical perspective on Hartree−Fock−Bogoliubov theory

Mathieu Lewin, Séverine Paul (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The method of choice for describing attractive quantum systems is Hartree−Fock−Bogoliubov (HFB) theory. This is a nonlinear model which allows for the description of pairing effects, the main explanation for the superconductivity of certain materials at very low temperature. This paper is the first study of Hartree−Fock−Bogoliubov theory from the point of view of numerical analysis. We start by discussing its proper discretization and then analyze the convergence of the simple fixed point (Roothaan)...

A partial regularity result for a class of stationary Yang-Mills in high dimension.

Yves Meyer, Tristan Rivière (2003)

Revista Matemática Iberoamericana

We prove, for arbitrary dimension of the base n greater than or equal to 4, stationary Yang-Mills Fields satisfying Borne approximability property are regular apart from a closed subset of the base having zero (n-4)- Hausdorff measure.

A partial solution for Feynman's problem – a new derivation of the Weyl equation.

Inoue, Atsushi (2000)

Electronic Journal of Differential Equations (EJDE) [electronic only]

A quantum-transport model for semiconductors : the Wigner-Poisson problem on a bounded Brillouin zone

Pierre Degond, Peter A. Markowich (1990)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A semi-classical picture of quantum scattering

Francis Nier (1996)

Annales scientifiques de l'École Normale Supérieure

A Two-Particle Quantum System with Zero-Range Interaction

Michele Correggi (2008/2009)

Séminaire Équations aux dérivées partielles

We study a two-particle quantum system given by a test particle interacting in three dimensions with a harmonic oscillator through a zero-range potential. We give a rigorous meaning to the Schrödinger operator associated with the system by applying the theory of quadratic forms and defining suitable families of self-adjoint operators. Finally we fully characterize the spectral properties of such operators.

Absence of geometrical phases in the rotating stark effect

Emanuela Caliceti, Stefano Marmi, Franco Nardini (1992)

Annales de l'I.H.P. Physique théorique

Absolute continuity of the spectrum of a Schrödinger operator with a potential which is periodic in some directions and decays in others.

Filonov, N., Klopp, F. (2004)

Documenta Mathematica

Absolute spectral continuity for N-body Stark hamiltonians

Erik Skibsted (1994)

Annales de l'I.H.P. Physique théorique

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